Stability of Wehrl-type Functionals and Concentration Estimates on Bergman Spaces of Log-Subharmonic Functions on the Unit Sphere
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| Format: | Preprint |
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2025
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| _version_ | 1866917151392137216 |
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| author | Jaguzović, Vladan Melentijević, Petar |
| author_facet | Jaguzović, Vladan Melentijević, Petar |
| contents | In this paper, we consider weighted Bergman spaces $\mathcal{B}_{α,p}$ of log-subharmonic functions on the unit sphere. Using the isoperimetric inequality for the spherical metric we prove certain monotonicity property for super-level sets of $|f(x)|^p\mathcal{W}_n^α(x),$ where $f\in \mathcal{B}_{α,p}$ and $\mathcal{W}_n^α(x)$ is the Bergman weight. As a consequence, we solve a maximization problem for certain Wehrl-type (convex) functionals and concentration estimates. Moreover, we show the stability of these estimates, proving that near-extremizing values are achieved for near-extremizing functions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_15193 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability of Wehrl-type Functionals and Concentration Estimates on Bergman Spaces of Log-Subharmonic Functions on the Unit Sphere Jaguzović, Vladan Melentijević, Petar Complex Variables Classical Analysis and ODEs Primary: 30H20, 30F15, Secondary: 31C12, 28A78 In this paper, we consider weighted Bergman spaces $\mathcal{B}_{α,p}$ of log-subharmonic functions on the unit sphere. Using the isoperimetric inequality for the spherical metric we prove certain monotonicity property for super-level sets of $|f(x)|^p\mathcal{W}_n^α(x),$ where $f\in \mathcal{B}_{α,p}$ and $\mathcal{W}_n^α(x)$ is the Bergman weight. As a consequence, we solve a maximization problem for certain Wehrl-type (convex) functionals and concentration estimates. Moreover, we show the stability of these estimates, proving that near-extremizing values are achieved for near-extremizing functions. |
| title | Stability of Wehrl-type Functionals and Concentration Estimates on Bergman Spaces of Log-Subharmonic Functions on the Unit Sphere |
| topic | Complex Variables Classical Analysis and ODEs Primary: 30H20, 30F15, Secondary: 31C12, 28A78 |
| url | https://arxiv.org/abs/2512.15193 |